# EconS Oligopoly - Part 1

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1 EconS Oligopoly - Part 1 Eric Dunaway Washington State University November 19, 2015 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

2 Introduction We are now ready to use some of the concepts that we learned during Game Theory and apply them to our previous models. Today, we are going to look at situations in which two rms with market power compete against one another. What will happen to the equilibrium? Does the type of competition matter? Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

3 Oligopoly Recall the assumptions of the perfectly competitive model: Free Entry and Exit Price Taking Homogenous Products Perfect Information Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

4 Oligopoly In oligopoly (Like monopoly, but with two or more rms wielding market power), the assumptions we will be using change into the following: Some barriers to Entry Market Power Homogenous Products Perfect Information Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

5 Oligopoly Before, in monopoly, we had just a single rm picking a quantity that led to a market price. Now, we have multiple rms selling an identical product and all of their quantities a ect the market price. If one rm produces a lot, it can hurt all of the other rms. We are going to look at several types of competition between rms, but before we get going, let s establish a base case. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

6 Cartel Pricing We have talked about cartels before. A cartel is where several rms work together to x a price higher than the perfectly competitive price. A cartel can maximize the total pro t for all of the rms. Basically, all of the rms will charge the same price as if they were a monopolist, and they achieve this by dividing up the monopoly quantity evenly among themselves. Let s look at an example. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

7 Cartel Pricing Consider a situation where two identical rms (a duopoly, we will mostly be focusing on these) coexisting in a market decide to form a cartel. They face the inverse demand curve p = 70 q 1 q 2 where q 1 denotes the quantity produced by rm 1 and q 2 denotes the quantity produced by rm 2. Both rms face a constant marginal cost of MC = 10. For simplicity, I could (in the cartel case) make a substitution of Q = q 1 + q 2 where Q represents the market quantity. This works because the rms are working together. The inverse demand function becomes p = 70 Q Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

8 Cartel Pricing From here, we follow the same steps as under monopoly. First, we need the marginal revenue, which comes from applying the power rule to the total revenue. TR = pq = (70 Q)Q = 70Q Q 2 MR = 70 2Q Next, we set marginal revenue equal to marginal cost, MR = MC 70 2Q = 10 2Q = 60 Q = 30 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

9 Cartel Pricing Plugging it back in to the inverse demand function, we get the market price, p = 70 Q = = 40 From here, we know that the total market output is equal to Q = 30. Since we have two rms, they each take an equal share of that output, and hence q 1 = q 2 = Q 2 = 15 This leads to total revenue and total cost for each individual rm (They will be the same since the rms are identical) of and pro ts of TR 1 = pq 1 = 40(15) = 600 TC 1 = 10q 1 = 10(15) = 150 π 1 = TR 1 TC 1 = = 450 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

10 Cartel Pricing Pricing as a cartel yields the highest total pro ts for the rms. The key is that we are looking at the joint pro ts of the rms, not individual pro ts. Perhaps there is a way for an individual rm to do better at the expense of the other rm? Of course there is. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

11 Cartel Pricing Why don t we see many cartels today? Why? Because they are self destructive. They re also illegal in most countries. There are too many incentives for individual rms in a cartel to cheat and take more of the market pro ts for themselves at the expense of their partners. In a more advanced game theory course, we could look at the level of "patience" a rm must have to sustain cooperation within a cartel. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

12 Cartel Pricing Why does OPEC survive? Recall OPEC (The Organization of Petroleum Exporting Countries) acts as a cartel for crude oil throughout the world. They survive because of Saudi Arabia. Basically, Saudi Arabia has implemented what is known as a Grim Trigger Strategy. If any member of OPEC cheats, Saudi Arabia will respond by ooding the market with cheap oil, destroying the pro ts for all the cartel members. Saudi Arabia can do this because they get their oil extremely cheaply, and they have a ridiculous amount of cash on hand (a war chest). The cheap oil prices in the last year may be the result of Saudi Arabia punishing some OPEC members (There are several other plausible reasons, too). Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

13 Bertrand vs Cournot In the 19th century, two economists proposed alternate ways for rms to compete. Louis Bertrand proposed that rms compete by setting prices. Antoine Cournot proposed that rms compete by setting quantities. They hated each other academically. We will analyze Bertrand competition today, and Cournot competition next time. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

14 Bertrand Competition As before, Bertrand Competition is where rms compete in prices. For simplicity, we will only consider the case where there are two rms, a duopoly, and they sell identical products. Each rm chooses a price, and the rm with the lowest price gets all of the customers. This is a very important assumption. In the case of a tie, the rms each get half of the customers. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

15 Bertrand Competition We will use game theory to determine each rm s optimal price. In this game, the rms are the players, and their strategies are the prices they choose. They move simultaneously and their payo s are their respective pro t levels. Like we learned in the bargaining game, prices are continuous variables. Let s look at rm 1 s best response function. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

16 Bertrand Competition We can break up rm 1 s best response function into three segments. When rm 2 s price is above the monopoly price. When rm 2 s price is between the marginal cost and the monopoly price. When rm 2 s price is below the marginal cost. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

17 Bertrand Competition p 1 p 1 = p 2 p M MC MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

18 Bertrand Competition The highest price that any rm would want to charge is the monopoly price. This is the price that each rm would charge if they were cooperating in a cartel. This price gives the highest level of pro ts if a single rm has all the customers. If rm 2 were charging a price above the monopoly price (which would be dumb, but we need to cover all of our cases), rm 1 would want to respond by charging exactly the monopoly price. They would get all of the customers and have the most pro ts possible. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

19 Bertrand Competition p 1 p 1 = p 2 p M MC BR 1 (p 2 ) MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

20 Bertrand Competition If rm 2 s price is between the marginal cost and the monopoly price, rm 1 has a few options: It could charge a price higher than rm 2 s and get no customers. It could charge a price equal to rm 2 s and get half of the customers. It could charge a price lower than rm 2 s and get all of the customers. Optimally, rm 1 would want to take the third option and get all of the customers. It also wants to charge the highest price possible to maximize its pro ts. This means that rm 1 s best response is to charge a price one unit (penny) lower than rm 2 s price. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

21 Bertrand Competition p 1 p 1 = p 2 p M MC BR 1 (p 2 ) MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

22 Bertrand Competition Lastly, if rm 2 s price is below marginal cost, rm 2 is actually losing pro ts with every unit sold. It would not be optimal to try and undercut them any further. Firm 1 s best response would then be to charge a price equal to marginal cost and accept zero pro ts. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

23 Bertrand Competition p 1 p 1 = p 2 p M MC BR 1 (p 2 ) MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

24 Bertrand Competition We can perform the same analysis to obtain rm 2 s best response function. Since rm 1 and rm 2 are identical, we will nd the exact same results. Let s plot rm 2 s best response function. Notice that I get this line by mirroring rm 1 s best response function across the p 1 = p 2 line. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

25 Bertrand Competition p 1 p 1 = p 2 p M BR 2 (p 1 ) MC MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

26 Bertrand Competition In order to nd our equilibrium, we just need to nd where the best response functions intersect. Intuitively, at this point the best responses for both rms align and neither rm has any incentive to deviate away from that price level. This will constitute a Nash Equilibrium. To nd this, we can plot the best response functions on top of one another. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

27 Bertrand Competition p 1 p 1 = p 2 p M BR 2 (p 1 ) MC BR 1 (p 2 ) MC p M p 2 Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

28 Bertrand Competition As we see in the gure, the only Nash Equilibrium is where both rms charge p 1 = p 2 = MC This is exactly the same as the perfectly competitive price. This leads both rms to receive zero economic pro ts in equilibrium. The consumers get it pretty good, though. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

29 Bertrand Competition This equilibrium should make sense. Firms will want to undercut one another until any further undercutting would result in negative pro ts. This happens where p = MC and pro ts equal zero. Next time, we ll look at what happens when rms compete in quantities. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

30 Summary When rms compete, they both have incentives to deviate from the monopoly price. Bertrand competition leads to both rms pricing at the perfectly competitive level. Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

31 Preview for Monday Cournot Competition Quiz 3 Have a great break! Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

32 Assignment 7-2 and 7-3 (1 of 1) 1. Consider a two rm duopoly that faces an inverse demand curve of p = 150 q 1 q 2 and constant marginal costs of MC = 60. a. If the rms behave as a cartel, what are the equilibrium quantities, price and pro ts for each rm? (Hint: They will be equal to one another) b. If the rms compete in prices (Bertrand competition), what are the equilibrium quantities, price and pro ts for each rm? (Hint: Also equal) Eric Dunaway (WSU) EconS Lecture 31 November 19, / 32

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